How does metallic bonding result in useful properties of metals?

When we think of covalent bonding in molecules, we assume the bonding (valence) electrons are shared between the two bonded atoms (only). This electrons, which "belong" to the bonded atoms are said to be localized.

In a metal, the valence orbitals overlap to form a continuous "sea" in which the valence electrons are free to travel through the entire metallic crystal. So, the bonding still involves positive atomic kernels (nucleus plus all non-valence electrons) which attracted to a sea of mobile valence electrons.

Applying only a small voltage across this crystal will cause the valence electrons to drift along the crystal from negative to positive, and electric current results.

The metal is malleable because stress applied to the crystal will cause the kernels to move relative to one another, but in such a way that the non-localized bonding maintains enough attraction that the crystal does not fracture.

Heat can also by conducted along the crystal because the same freedom of motion in the kernels and bonding electrons allows for kinetic energy to pass along the crystal.

Reflectivity is due to the fact that the energies of the non-localized electrons form a conduction "band" of energies, and allow for light of all frequencies to be absorbed and released, but this a only a glimpse into a lengthy topic!

Hope this helps!